Question

A simple pendulum is taken to mountain so that the acceleration due to gravity falls to 1/16 find its new time period?

Answer 1

Given:

A simple pendulum is taken to mountain so that the acceleration due to gravity falls to 1/16 times.

To find:

New time period of pendulum.

Calculation:

Time period of a simple pendulum is given by the following formula :

$\boxed{ \sf{T = 2\pi \sqrt{ \dfrac{l}{g} } }}$

At a new altitude , the new gravitational acceleration becomes g/16.

$\sf{T2 = 2\pi \sqrt{ \dfrac{l}{ (\frac{g}{16} )} } }$

$\sf{ = > T2 = 2\pi \sqrt{16 \times \dfrac{l}{g} } }$

$\sf{ = > T2 =4 \times \bigg \{ 2\pi \sqrt{\dfrac{l}{g} } } \bigg \}$

$\sf{ = > T2 =4 \times T }$

So the new time period of the pendulum is 4 times the original time period.